The ratio of athletes in the two teams is 3:2. After 12 athletes move from first team to second, the ratio is 5:4. Find the numb

Question

sergij07 [2.7K]

2 years ago

7

The ratio of athletes in the two teams is 3:2. After 12 athletes move from first team to second, the ratio is 5:4. Find the numb

er of athletes on each team originally.

Mathematics

2 answers:

GaryK [48] · Answer 1 · 2022-10-24T23:36:05+03:00

Answer:

162 athletes
108 athletes

Step-by-step explanation:

Each ratio can be expressed using two numbers that have the same sum. The sum in the first given ratio is 3+2 = 5, and in the second ratio, it is 5+4 = 9. The least common multiple of 5 and 9 is 45, so we can express both ratios so they have a sum of 45:

3 : 2 = 3(9) : 2(9) = 27 : 18

5 : 4 = 5(4) : 4(5) = 25 : 20

Here, we observe that the second ratio has numbers that look like 2 was moved from the numerator to the denominator. (27 -2 = 25; 18 +2 = 20) The problem statement tells us 12 athletes were moved, so multiplying the first ratio by 12/2 = 6 will tell us the numbers of players on each original team:

first team = 27×6 = 162 athletes

second team = 18×6 = 108 athletes

Alex · Answer 2 · 2022-10-24T21:11:59+03:00

Answers:

team one = 162
team two = 108

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Explanation:

The ratio 3:2 scales up to 3x:2x for some positive whole number x.

This tells us that the first team has 3x people and the second team has 2x people. We'll subtract 12 from the first team and add 12 to the second team to represent 12 people moving.